Beginning Math and Physics for Game Programmers
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Chapter 6, "Transformations"
2D Translation by Addition
where dx = change in x and dy = change in y . 3D Translation by Addition
where dx = change in x, dy = change in y , and dz = change in z . 2D Translation by Multiplication
where dx = change in x and dy = change in y . 3D Translation by Multiplication
where dx = change in x, dy = change in y , and dz = change in z . 2D Scaling
where Sx = scale factor in the x direction and Sy = scale factor in the y direction. 3D Scaling
where Sx = scale factor in the x direction, Sy = scale factor in the y direction, and Sz = scale factor in the z direction. 2D Rotation
where q is the angle of rotation. 3D Rotation About the z-Axis (Roll)
where q is the angle of rotation. 3D Rotation About the x-Axis (Pitch)
where q is the angle of rotation. 3D Rotation About the y-Axis (Yaw)
where q is the angle of rotation. 2D Combo Matrix
For every 2D combo matrix entries with an r store scaling and rotation information, and entries with a t store overall translation information. 3D Combo Matrix
For every 3D combo matrix entries with an r store scaling and rotation information, and entries with a t store overall translation information. Conversion Between OpenGL and DirectX Formats
AB = B T A T for matrices A and B: |
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